Quick answer: Harmony Navigator and Synfire are powerful tools that enable you to dig deep into harmony. The main difference is the approach taken by the designer of the software for the user interface, which enables very complex interactions in harmony. This results in a more complex handling than Liquid Notes.
How Liquid Notes differs from Harmony Navigator or SynfireHarmony Navigator and Synfire, both developed by Cognitone, are two powerful pieces of software to help you arrange songs and compose music for any style.
In Harmony Navigator, harmonic progressions can be assembled by choosing chords from a palette of available chords, by manually inputting chord symbols or by recording and interpretation of MIDI input. A host of complex choices and functions allow for experimenting, editing on the overall, as well as the detailed handling of content within the software.
All knowledge, all intelligent decisions and analyses are based on an internal "Harmony Catalog" which can be customized by the user.
As opposed to Liquid Notes, Harmony Navigator does not support the import, analysis and treatment of MIDI files (neither self created nor third party). Further, Harmony Navigator LE limits the number of instrument tracks to a maximum of four.
Sounds (up to maximum of four instruments) are assigned via transmission to external synthesizers and sound generators in MIDI format.
Harmony Navigator can not host AU/VST plugins directly itself. If the sounds of virtual instruments (VST/AU plug-ins) are desired, these need to be loaded into a host software (DAW, sequencer, rack) and Harmony Navigator's MIDI output needs re-directing to the host by means of a MIDI Loopback Driver. Harmony Navigator sends all output to that driver, which in turn sends it back to the host.
Advanced versions, such as Harmony Navigator Advanced and Synfire Express/Pro, progressively support further options such as melody harmonization, figure recognition, an increased number of instruments, syncing to DAWs using ReWire (however DAW control is limited mostly to transport), MIDI file import and plugin hosting (Synfire) and a variety of rather complex processes akin to melodic composition and music creation.
While the capabilities of the Cognitone's range of softwares, especially Synfire Pro, are impressive indeed, the overall handling is seriously complex, demanding and distinctively different from Liquid Notes, whose aim it is to manage harmonic analysis and manipulation on single- or multi-track level in the most efficient, yet flexible manner. Liquid Notes is clearly different in concept and makes it possible to achieve excellent results without necessarily having to know much or anything about chords or harmonic progressions and with a minimum of technical involvement.